modeling with foundations and surrounding ground has to be reduced due to factors inherent in a large facility, such as the caacity of the shake table

Transcription

1 京都大学防災研究所年報第 54 号 B 平成 3 年 6 月 Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 54 B, Alication of the Generalized Scaling Law to Liquefiable Model Ground Tetsuo TOBITA, and Susumu IAI Synosis A series of centrifuge model tests are conducted under the scheme of the modeling of models technique to find issues on the generalized scaling law for dynamic centrifuge tests (Iai et al., 5). In a series of dynamic tests on a flat, saturated sand layer of / scale, four different centrifugal accelerations from 5 g to 7 g are emloyed on the scaled models for which the rototye is uniquely given. The models are exosed to sinusoidal inut accelerations with.65 Hz and amlitudes of.5 m/s and 3. m/s in rototye scale. For resonse during shaking, nearly identical accelerations and excess ore-water ressure buildus are recorded for all the cases in the rototye scale. Discreancies are found on surface settlements and duration time for dissiation of excess ore-water ressure. The major causes of the discreancy may be () the duration time for the initial consolidation, () small value of the shear modulus due to low confining stress in model ground under low centrifugal acceleration, and (3) reduced ermeability due to adsortion of viscous fluids on sand articles.. Introduction Alication of the geotechnical centrifuge modeling to design ractice was considered in the ast (e.g., Craig, 984); however, with increasing demands on erformance-based design of large structures, hysical model testing seems to be facing limitations due to modeling techniques and equiment. This is where the breakthrough for hysical modeling can be addressed as to directly aly test results of large rototyes to erformance-based design ractice. This may be one of the challenging toics for the geotechnical centrifuge community to be linked with industry (Terashi et al., 4; Gaudin et al., ). One of the great advantages of numerical analyses is that resonse of full-scale structures can be readily simulated, and arametric studies can be conducted just by changing numbers in inut files. However, numerical methods are solely validated through results of hysical model tests or real-scale behavior of geotechnical structures. Desite the fact that results of numerical analyses are merely an aroximation, they have often been used for quantitative evaluation of structural behaviors without comaring results of comutation with other numerical or hysical models. Use of a geotechnical centrifuge has an advantage in accurately simulating real-scale behavior in a scaled model by alying the same confining stresses to the model ground as rototyes. In the centrifuge model testing, although structural models have to be small and simlified, the rototye behavior is aroximated in accordance with scaling laws (e.g., Garnier et al., 7), and it qualitatively reresents rototye behavior. One of the major obstacles for alication of hysical modeling results to erformance-based design ractice is that a secific rototye cannot be tested due to restrictions associated with exerimental conditions, such as the size of the model container and scaling effects on materials. For -g model testing, to overcome these restrictions, the size of the exerimental facility has become larger and larger so that real-scale models can be tested [e.g., E-defense (Tokimatsu et al., 7), U.C. San Diego (Einde et al., 4)]. However, for geotechnical structures, develoment of a larger research facility may still have limitations because, even with such a large facility, hysical 5

2 modeling with foundations and surrounding ground has to be reduced due to factors inherent in a large facility, such as the caacity of the shake table, budget, etc. Demands for the testing of large rototyes are increasing under the restrictions mentioned above. To resolve such demands and restrictions, Iai et al. (5) roosed the scaling law by combining the scaling law for centrifuge testing with the one for -g dynamic-model testing. They call it the generalized scaling law in dynamic centrifuge modeling. The objective of the resent study is to investigate and oint out issues on the alicability of the scaling law through the technique of modeling of models for dynamic behavior of flat, saturated sand deosits.. Brief review of the generalized scaling law Scaling factors for hysical model tests can be introduced in general forms by choosing a set of basic hysical roerties to be indeendent and deriving the scaling factors for other roerties via governing equations of the analyzed system. These rimitive forms of scaling factors are listed in row (4) in Table. In the concet of the generalized scaling law, a model on a shaking table in a geotechnical centrifuge is considered to be a small-scale reresentation of a -g shaking-table test. Figure visualizes this concet by introducing a virtual -g model to which the rototye is scaled down via a similitude for -g shaking-table tests (Iai, 989). The virtual -g model is subsequently scaled down by alying a similitude for centrifuge tests to the actual hysical model. In this way, the geometric scaling factors alied in -g tests (μ) [row () of Table ] can be multilied with those for centrifuge tests (η) [row () of Table ], resulting in much larger overall scaling factors λ=μη [row () of Table ]. Table. Scaling factors (= Prototye/Model) in hysical model tests () scaling factor for g test () (3) scaling factor artitioned for centrifuge scaling factor test (4) generalized scaling factors Length μ η μη λ Density Time μ.75 η μ.75 η (λλ ε /λ g ).5 Frequency μ.75 /η μ.75 /η (λλ ε /λ g ).5 Acceleration /η /η λ g Velocity μ.75 μ.75 (λλ ε λ g ).5 Dislacement μ.5 η μ.5 η λλ ε Stress μ μ λλ g Strain μ.5 μ.5 λ ε Stiffness μ.5 μ.5 λλ g /λ ε Permeability μ.75 η μ.75 η (λλ ε /λ g ).5 Pore ressure μ μ λλ g Fluid Pressure μ μ λλ g Table. Generalized scaling factors imlemented in the resent study Scaling factor (Prototye/Model) G:.43 Centrifuge: Length Density.... Time Frequency Acceleration Velocity Dislacement Stress Strain Stiffness Permeability Pore ressure / MODEL VIRTUAL G PROTOTYPE /η /μ μ = /η Figure. Concet of modeling of models alied to the generalized scaling.. Dynamic centrifuge tests on flat loose, saturated sand deosit To investigate the alicability of the generalized scaling relations described above, a 6

3 Table 3. Test cases with scaling factors, roerties of inut motion, measured relative density and time for consolidation before shaking series of dynamic tests was conducted following the rincile of modeling of models. This technique was introduced by Schofield (98) to assess the behavior of a rototye through reetition of the test at different scales and comarison of the results in rototye scale. In the resent study, without changing the actual size of the hysical model but varying the virtual -g dimension, the overall scaling factor (λ=μη) is ket constant (Fig. ). Here, it is set to a fixed value comrising different combinations of the scaling factors for -g model testing, μ, and centrifuge testing, η. Table lists the alied geometric scaling factors as well as frequencies and amlitudes of the inut motions emloyed in the study. In what follows, units are in rototye unless otherwise secified.. Test cases Test cases are summarized in Table 3. In the test series referred to Case A, centrifuge tests under 5,, 5, and 7 g were emloyed with the target amlitude of the inut acceleration of.5 m/s. In the tests referred to Case B, centrifugal accelerations of 5,, and 5 g are carried out with the target amlitude of the inut acceleration of 3. m/s. Inut waves are sinusoidal, and their frequency is fixed at.65 Hz, and duration is 35 s. Note, for examle, that a case secified by 5B89 in Table 3 indicates that the centrifuge test was conducted in 5 g with 8.9 min of consolidation time in model scale in Case B. Here, the time for consolidation is the duration time given to the model to have a normally consolidated condition under secified centrifugal acceleration before shaking.. Test setu and exerimental facilities The tests were conducted in the geotechnical centrifuge of the Disaster Prevention Research Institute, Kyoto University, Jaan, which has an arm length of.5 m and is equied with a shaking table that allows us to exose the models to dynamic excitation in the tangential direction of flight. The instrumentation of the model is shown in Fig.. The strong box with inner dimensions of 45 cm by 5 cm (model scale) in width was filled u to an intended height of 5 cm (model scale) corresonding to a 5-m-dee sand deosit in rototye scale. Acceleration was measured at six different deths of the model (Fig. ). Also, with deth, five excess ore-water ressure transducers and two earth ressure transducers were installed at the locations secified in Fig.. Surface settlements were continuously measured with three laser-dislacement transducers attached above the ground surface (Fig. ). Reflection lates as targets of the laser-dislacement transducers were hand-made with the density of the late adjusted to slightly heavier than that of the mixture of viscous fluid so that it followed the surface settlements (Fig. ). The height of the ground surface was also manually measured at 8 oints before and after shaking. 7

4 The temerature of the model ground was monitored by digital thermometers to have the secific viscosity of the ore fluid [Metolose (Shin-Etsu Chemical Co., 997)], which is known to be highly temerature-deendent LD left LD middle LD right T T Target of LD EP EP 8 8 AC5 AC4 AC3 AC AC AC Figure. Test setu. LD: Laser dislacement transducers. AC: Accelerometers. PW: Pore-water ressure transducers. EP: Earth ressure transducers. T: Thermometers..3 Material of the model ground The model ground was reared with the method of water luviation. Dry silica sand No. 7 was srinkled slowly into high viscous water from aroximately cm (model scale) above water level. The relative density in the models varied between 4% and 33% in Case A, and 44% and 47% in Case B. Although the total weight of sand in the box was ket constant, a slight difference in achieved height of the model ground caused variation of the relative density. According to the scaling factors in Table, the viscosity of the ore fluid has to be scaled with a factor, μ.75 η, relative to water. This leads to the use of higher viscous water in all tests than that of usual centrifuge model tests. To roduce water with the secific viscosity for each test, the methylcellulose solution (Metolose, SM-) is emloyed. The usability of the Metolose to roduce high viscous water without changing other significant fluid arameters such as density or surface tension was tested and verified u to mpa s (Dewoolkar et al., 999; Stewart et al., 998). As the viscosity of the Metolose solution is highly deendent on the water temerature, it was Ideal filling height: 5 AC measured and adjusted by adding water or denser solution before ouring it into the strong box. 3. Resonse of the model ground 3. Inut and ground acceleration To fulfill the urose of the exeriments, it is imortant to give the identical inut motions in rototye scale for all of the test cases. Following the scaling relations of acceleration and frequency shown in Table, the inut amlitude and time scale of acceleration for each test in model scale are determined (Table 3). At the bottom row of Fig. 3(a), lotted are time histories of inut accelerations in model scale. By alying the generalized scaling factors of acceleration and time to those time histories, they are converted into the ones shown in the bottom row of Figure 3(b). As shown in these figures, although amlitudes and durations of shaking of the inut acceleration in model scale are different, in rototye scale fairly similar inut accelerations are obtained for all of the tests in both cases. This guarantees that nearly identical inut acceleration was given to each model. Note that in the test A5 by mistake the frequency of the inut motion was a little smaller than the aimed value (34.57 Hz instead of Hz). Judging from the figures, the influence should be minor. In the same way as the inut motion mentioned above, time histories of accelerations in the model ground are lotted in Fig. 3 for Cases A. In both cases, accelerations near the ground surface in rototye scale [Figs. 3(b)] show reduction of the amlitude due to liquefaction. The enveloe of the time histories in rototye scale are satisfactorily similar to one another, desite the small variation in the relative density of the model ground (Table 3). 8

5 Figure 3(a). Measured time histories of acceleration in model scale for Case A. Figure 3(b). Measured time histories of acceleration in rototye scale for Case A. 3. Excess ore-water ressure Time histories of excess ore-water ressures are comared in Figs. 4 and 5 for Cases A and B, resectively. Figures 4(a) to 4(e) show excess ore-water ressure buildu during shaking, and Figs. 4(f) to 4(j) show those until full dissiation. As shown in Figs. 4(a) to 4(e), agreements are significant for all of the cases, excet for case 7A5. In 7A5, by considering that the inut and ground accelerations are very similar to the others [Fig. 3(b)], ore-water ressure transducers might be malfunctioning, and ossibly they were not erfectly saturated. For Case B in Figs. 5(a) to 5(e), agreements are significant, excet for the tests 5B5 and B5, in which ceramic filters (5. mm thick) whose oening is much smaller than metal mesh (55-m oening) was attached on the ore-water ressure transducers. Therefore, sensitivity was lost. As shown in Figs. 4(f) and 4(g) for tests 5A5 and A5, the time required for full dissiation is much longer than in the other cases. The same may be said for test 5B5 and B5 in Case B, shown in Figs. 5(f) to 5(j), comared with the one shown in Fig. 5(j) for test 5B5. The cause of this will be investigated later. 9

6 PW PW PW 3 PW 4 PW 5 (f) 5A5 5 (b) A5 (g) A5 5 5 (c) 5A5 (h) 5A5 5 5 PW PW PW 3 PW 4 PW 5 (d) 7A5 5 5 (e) 7A5-7A5- (e) 5 (j) 7A (s) Time Figure 4. Measured time histories of excess ore-water ressure in rototye scale for Case A: (a) to (e) in the hase of ressure buildu ( 5 s), and (f) to (j) in the hase of dissiation (entire record). 5 (g) 5B89 (c) B5 (h) B5 5 5 (d) B75 5 (i) B75 5 (e) 5B5 5 (j) 5B Figure 5. Measured time histories of excess ore-water ressure in rototye scale for Case B: (a) to (e) in the hase of ressure buildu ( 5 s), and (f) to (j) in the hase of dissiation (entire record). (d) LD-Left (a) DL-Left time [s] Settlement (mm) 5A5 3 A5 Time [s] 6 8 A5 7A5 5A5 (e) LD-Center Time [s] A5-7A5 A5 5A5 5A5 3 4 Time [s] 6 8-7A5 7A5-5A5 5A5 3 A5 4 4 (c) LD-Right (f) LD-Right Time [s] 6 8-5A5 7A5 5A5 g A5 7A5-7A A5 7A5 A5 5A5 3 5A5 7A5-4 - Settlement (mm) 4 3 7A5 (b) LD-Center - 7A5-5A5 4 Settlement (mm) 3.3 Ground settlements For the time range in dynamic excitation, the generalized scaling law can be verified for all reorted asects of soil behavior excet for the ground settlements measured with laser dislacement transducers which showed a big scatter among the models. Figure 6 shows those for Case A. In these figures, (a) to (c) are the ground settlements during shaking, and figures (d) to (f) are those until nearly comlete dissiation of the excess ore-water ressure. The variations seem to be comletely random. The variation observed in the ground settlements may be attributed to the device used in the tests and/or large scaling factors for dislacement. The target late of the laser dislacement transducer might be influenced by the shaking because of its height, which is 3 cm in model scale (Fig. ). Another cause may be that the scaling factor of dislacement in the generalized scaling law is much larger, i.e., sensitive, comared with other scaling factors (Table ). Therefore, secial care had to be taken in the measurements of ground settlements [e.g., article image velocimetry (b) 5B89 5 (f) 5B5 (a) 5B5 5 (i) 7A5 Excess ore water ressure (kpa) Excess ore water ressure (kpa) Settlement (m) Settlement (m) (a) 5A5 5 (PIV) (White et al., 3)]. As shown in Fig. 6, the duration of settlements after shaking for tests 5A5 and A5 in Case A is much longer than the other cases with higher centrifugal accelerations. A similar trend can be seen in tests 5B5 and B5 in Case B i.e., saturating the model ground with lower centrifugal acceleration tends to take more time for full settlements and give larger residual settlements. Settlement (m)

7 Figure 6. Measured time histories of ground settlements in rototye scale for Case A: (a) to (c) in the hase of shaking ( 5 s), and (d) to (f) in the hase of dissiation (entire record). 4. Causes of discreancy at low centrifugal acceleration The two cases that were run at 5 g and g showed much larger settlements and a longer duration time for ore-water dissiation in rototye scale than the others with higher centrifugal accelerations. In what follows, investigations are carried out to seek causes of the low rate of dissiation of excess ore-water ressure. Here, the following causes are assumed and examined in detail: () effects of duration time for consolidation before shaking, () effect of low effective confining stress on the scaling law, and (3) ossible change of ermeability of the model ground due to adsortion of the Metolose olymers on sand articles. 4. Effects of duration time for consolidation before shaking In the centrifuge exeriments, to have a normally consolidated ground under the given centrifugal acceleration, the model ground is consolidated about 5 min before shaking. This 5 min is arbitrarily taken because consolidation of sandy ground is assumed to be quickly achieved. However, with viscous fluid, this assumtion may be a mistake. In tests 5B5 and B5, fluid viscosities are, resectively, 47.3 mpa s and 56. mpa s, and the duration times of consolidation are converted, resectively, to 8 min and 37 min in rototye scale, which is much shorter than that of 5B5 4 min. In Case B, tests 5B89 and B75 are the cases in which the duration time of consolidation is adjusted so that the same duration time with test 5B5 is alied in rototye scale. In tests 5B89 and B75, duration times for consolidation were, resectively, 8.9 min and 7.5 min in model scale. As shown in Fig. 5(g) for 5B89 and Fig. 5(i) for B75, dissiation of excess ore-water ressure becomes quicker than in the cases of 5B5 and B5 and aroaches the ones of 5 g s [Fig. 5(j)]. Although the duration time of consolidation is adjusted, a erfect match is not achieved, indicating the existence of other causes on the discreancy. 4. Effect of low effective confining stress on the scaling law The curves in Figs. 4(f) to 4(j) and Figs. 5(f) to 5(j) indicate that time required for excess ore-water dissiation becomes systematically shorter as the centrifugal acceleration increases. Model behavior in dissiation hase can be exlained by the consolidation theory from which the following formula for time for consolidation is derived: Td v mv w Td v w t () k Mk where T v : time factor, d: length of longest drainage ass, m v : volume comressibility (= /M), M: constrained modulus of elasticity ( G( )/( ) ), G: shear modulus, : Poisson ratio, w : unit weight of water, and k: ermeability. In the exeriments under low centrifugal accelerations, the effective confining stress in model scale is low in the dissiation hase, and this may lead to a smaller stiffness of the model ground. From Eq. (), small elastic stiffness leads to a long eriod of time for consolidation. Thus, scaling of stiffness might have an influence on the time of the ore-water dissiation. In what follows, to investigate the scaling of stiffness under low effective confining stress, a scaling factor of strain in the -g model test is derived by fitting with exerimental results. The scaling relation of time in general form is exressed from row (4) in Table : t /.5 g () where,, and g are, resectively, the scaling factor of length, strain, and acceleration. In -g model tests, g, and if the scaling.5 factor of strain is assumed to be (Iai, 989), then the scaling factor of time is derived from Eq. () as.75 t (3) For the scaling of centrifuge tests, g /, and, and therefore the scaling of time is 3

8 derived again from Eq. () to be (4) t When the scaling factor of a -g test is, and that of a centrifuge test is, the generalized scaling factor of time is given as a combination of the above two factors (Iai et al., 5):.75 t (5) In addition to the assumtion made for the scaling factor of strains, Iai (989) showed that when the shear-wave velocity is known, can be determined more accurately with the following form: (6) Vs / Vs m where ( V s ) and ( V s ) m are, resectively, the shear-wave velocity of the rototye and the model. From Eq. (6), it is evident that the scaling of stain is closely related to shear-wave velocity, which can be readily converted to the shear modulus of the ground. Now, let us assume that the scaling factor of strain can be exressed with as (7) Then, from Eq. (), scaling of time becomes.5( ) t (8) Scaling of time for the generalized scaling relation is exressed as t.5( ) tm (9) where t and t m are, resectively, time in the rototye and the model. Next, arameter is fitted with exerimental results. Here, the duration time for the excess ore-water dissiation measured at 7 of test 7A5-, t, in rototye scale, is taken as a reference value to be fitted. Then, by assuming that the duration times for dissiation at of other tests, t, in rototye scale, are equal to : 7 t t t () 7 Rewriting Eq. () with the generalized scaling factors given in Eq. (9), with time in model scale, 7 t m and t m, t t ().5( ).5( ) 7 m 7 7 m where 7.4 and 7 7 are scaling factors, resectively, in the virtual -g and 7-g centrifuge model tests. Here, the duration time for dissiation in model scale is defined as, t t t () m where t corresonds to the time when the excess ore-water ressure at starts to decrease [Figs. 7(a) (d)] and t is defined at the time when the excess ore-water ressure becomes 5% of the one at time t. Solving Eq. () for yields 7 7t m log log tm 7 (3) Table 4 shows the comuted value of by substituting by and 7 into Eq. (3). t m t m In Table 4, the shear-wave ratio is comuted ( ) / V / V s s m (4) and the ratio of shear modulus G /G m is comuted by taking the square root of Eq. (4), where G and G m are, resectively, the shear modulus in rototye and model scale. Figures 7 (a) to 7 (d) show time histories of excess ore-water ressure in model scale. In these figures, duration time for dissiation is indicated by dotted vertical lines. Figures 7(e) to 7(h) are the converted time histories in rototye scale with fitted scaling factors of time listed in Table 4. Here, the scaling for stress i.e., the magnitude of excess ore-water ressure is not affected by the fitting rocedure. Ratios of the shear modulus comuted with the fitted arameter in Table 4 show that if the -g scaling factor of strain is given as i.e., =.5, then the ratio is assumed to be G /G m =.96. In this case (7A5-), it is recognized that the stiffness of the model and the rototye are nearly equal. For tests with low centrifugal accelerations, 5A5 and A5, the values of are negative, and the ratios are comuted to be G /G m (5 g) =.5 3

9 ground under low centrifugal acceleration. (a) 5A5 (model) (e) 5A5 (rototye) tm Excess ore water ressure (kpa).4 and G/Gm( g) =.3, which is about two times the one obtained from test 7A5-, G/Gm(7 g) =.5 (Table 4). From this comutation, if we demand that the shear modulus in rototye scale is constant regardless of the level of centrifugal acceleration, then the shear modulus under low centrifugal acceleration has to be about half of that under high centrifugal acceleration [e.g., Gm(7 g) =.Gm(5 g)]. Thus, in the exeriments conducted under low centrifugal acceleration, shear modulus or elastic modulus of the model ground in model scale has to be adjusted smaller than that in high centrifugal accelerations so that an identical duration time of excess ore-water ressure dissiation is achieved in rototye scale. The fitting for Case B is done by the same rocedure by taking the same value of the test 7A5- as a reference. In Table 4, the values of arameter for tests 5B89 and B75 are, resectively,.43 and., and the shear modulus ratios are, resectively, G/Gm(5 g) =.53 and 3 (b) A5 (model) 7 (f) A5 (rototye) tm (g) 5A5 (c) 5A5 (model) (rototye) tm 5 (d) 7A5- (model) 35 7 (h) 7A5- (rototye) tm Figure 7. Time histories of excess ore-water ressure build-u for Case A: (a) to (d) model scale, (e) to (h) fitted curves in rototye scale. (h) is shown in Fig. 5(j). Table 4. Parameters for correction of time scaling in the hase of excess ore-ressure dissiation G/Gm( g) =.59, which are smaller than those obtained from tests 5A5 and A5 and close to the one in 7A5- [G/Gm(7 g) =.5]. Again, if we demand that shear modulus in rototye scale is identical, we obtain Gm(7 g) =.4Gm(5 g) and Gm(7 g) =.5Gm( g). Thus, to achieve identical duration time for dissiation of excess ore-water ressure with the one under high centrifugal acceleration, the shear modulus in model scale under low centrifugal acceleration has to be larger than that in rototye scale. The discreancy investigated in this section may be due to the small value of the shear modulus caused by the low confining stress in the model 4.3 Possible change of ermeability of the model ground due to absortion of the Metolose on sand articles In the exeriment, the Metolose (methylcellulose) was used as a substitute for ore fluid so that scaling for excess ore-water ressure dissiation is satisfied with dynamic conditions (Ko, 994; Stewart et al., 998; Dewoolkar et al., 999). It is known that the viscosity of the methylcellulose is exerted by long chains of micro-fibers (olymers) constituted of cellulose (Stewart et al., 998). Because of the form of micro-fibers, absortion of the Metolose on sand articles might occur. To investigate the 33

10 ossibility, falling head ermeability tests for silica sand No. 7 with a relative density of 4% with water, Metolose solution, and silicone oil were conducted. To conduct the tests, the rocedure secified by JIS A 8:9 was followed. A metal-mesh net with a 75-m oening was used as a filter instead of using filter aer in order to revent clogging of molecular cellulose. Metolose of % solution was reared and adjusted to secific viscosity by adding water. Details of tests can be found elsewhere (Tobita and Iai,, under rearation). Test results are summarized in Fig. 8. As shown in Fig. 8(a), the ermeability of water is ket constant at about. - cm/s. The reduction of ermeability after the th measurements with water is -4.7%, which can be regarded as no reduction. Meanwhile, as shown in Figs. 8(b) and 8(c), the ermeability with the Metolose is consistently decreasing with the number of measurements. For examle, the ermeability of viscous fluid of 5 mpa s is decreased 44% from.46-3 cm/s to cm/s after the th measurements. In Fig. 8(d), although the ermeability of silicone oil is fluctuating, the ermeability is nearly constant for each viscosity. The reduction in ermeability that may be achieved with an increase in ore-fluid viscosity is mostly smaller than the exected values. For examle, a reduction in ermeability by a factor of.4 was recorded for an increase in viscosity of 5 times. This trend has been reorted in other research aers (Stewart et al., 998; Dewoolkar et al., 999). Stewart et al. (998) gave ossible exlanation for this discreancy that both the Metolose solution and silicone oil may exhibit non-newtonian behavior, where viscosity is not constant with varying velocity gradients. If this is the case, the reduction ratio of ermeability would be different than that of the inverse viscosity ratio. Based on the ermeability test data, the ermeability of the model ground during the centrifuge exeriments might be slightly decreasing as excess ore-water ressure dissiates with the flow of the viscous fluid. However, no clear trend is found on the ermeability change with the magnitude of viscosity. Further investigation is necessary to identify the effect of the absortion on the reduction of ermeability. Permeability (cm/sec) Permeability (cm/s).5e-.e- 5.E-3.E-4 3 mpa sec 45 mpa sec Silica sand No. 7, Dr=4% mpa sec.e+.e E-3 4.E-3 3.E-3.E-3.E-3 (a) Water (b) Met. cellulose Figure 8. Variation of ermeability with the number of measurements: (a) water, (b) methylcellulose of 5 and 5 mpa s, and (c) methylcellulose of 3, 45, and mpa s, and silicone oil of 3, 5, mpa s. 5. Conclusions 5 mpa sec 5 mpa sec 6.E-4 5.E-4 4.E-4 3.E-4.E-4 6.E-4 5.E-4 4.E-4 3.E-4.E-4.E-4 (c) Met. cellulose (d) Silicone oil Silica sand No. 7, Dr=4% Silica sand No. 7, Dr=4% 3 mpa sec 5 mpa sec Silica sand No. 7, Dr=4% mpa sec.e+.e Number of measurements Number of measurememts To investigate the alicability of the generalized scaling law in dynamic centrifuge tests on a flat, saturated sand deosit, the modeling-of-models technique was imlemented in centrifugal accelerations ranging from 5 to 7 g, and the results were comared in rototye scale. In the tested range of an overall scaling factor of /, the alicability of the generalized scaling law was confirmed for the time range during dynamic excitation. Only the ground settlement in this time range varied among the cases with different centrifugal accelerations. One of the causes might be the target device for the laser dislacement transducers, which might not be stable under shaking conditions. Additional care has to be given to measurements of dislacement because in the generalized scaling law the scaling factor of dislacement tends to be very large, and in turn very sensitive to the measurements. In the time histories of ore-water dissiation and surface settlements, two cases below g showed much larger duration time for 34

11 excess ore-water ressure dissiation. Investigations are carried out for () the effect of duration time for consolidation before shaking, () the effect of low effective confining stress on the scaling law, and (3) ossible change of ermeability of the model ground due to absortion of methylcellulose olymer on sand articles. A major cause of the discreancy might be the small value of elastic stiffness due to low confining stress in the model ground under low centrifugal exeriments. From results of the ermeability tests, use of the Metolose to simulated dissiation behavior is questioned because of the ossibility of the absortion on sand articles. Acknowledgements The authors acknowledge that exerimental works reorted in the resent aer are mainly conducted by Ms. Loretta von der Tann (former graduate student at ETH Zurich, Switzerland, visiting research student at Kyoto University, Jaan) and Mr. Yuji Yaoi (current graduate student at Kyoto University, Jaan.) as art of their graduation thesis. References Craig, W. H. (984), Centrifuge modelling for site-secific rototyes. Proc. Sym. Alication of Centrifuge Modelling to Geotechnical Design, University of Manchester, Balkema, Rotterdam, Dewoolkar, M. M., Ko, H.-Y., Stadler, A. T. and Astaneh, S. M. F. (999), A substitute ore fluid for seismic centrifuge modeling. Geotechnical Testing Journal, ASTM (3), 96. Einde, V. D., Restreo, L., Conte, J. P., Luco, E., Seible, F., Filiatrault, A., Clark, A., Johnson, A., Gram, M., Kusner, D. and Thoen, B. (4), Develoment of the George E. Brown Jr. network for earthquake engineering simulation (NEES) large high erformance outdoor shake table at the University of California, San Diego. Proceedings of the 3th World Conference on Earthquake Engineering, Vancouver, BC, Canada, -6 August, Paer No. 38. Garnier, J., Gaudin, C., Sringman, S. M., Culligan, P. J., Goodings, D., Konig, D., Kutter, B., L., Phillis, R., Randolh, M. F. and Thorel, L. (7), Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling. International Journal of Physical Modelling in Geotechnics, 7, No. 3, 3. Gaudin, C., White, D. J., Bezuijen, A., Schaminee, P. E. L. and Garnier, J. (), Physical modelling with industry overview of ractices and benefits, Physical Modelling in Geotechnics, Sringman, Laue & Seward (eds.). Taylor & Francis Grou, London, ISBN Iai, S. (989), Similitude for shaking table tests on soil-structure-fluid model in g gravitational field, Soils and Foundations, 9(), 5 8. Iai, S., Tobita, T. and Nakahara, T. (5), Generalized scaling relations for dynamic centrifuge tests, Géotechnique, 55(5), Ko, H.-Y. (994), Modeling seismic roblems in centrifuges, Centrifuge 94, Leung, Lee & Tan (eds.), Balkema, Rotterdam, ISBN No. 3-. Schofield, A. N. (98), Cambridge geotechnical centrifuge oerations, Géotechnique, 3(3), Shin-Etsu Chemical Co., L. (997), Metolose Brochure, Cellulose Det., 6-, Ohtemachi -chome, Chiyoda-ku, Tokyo, Jaan. Stewart, D. P., Chen, Y.-R. and Kutter, B. L. (998), Exerience with the use of Methylcellulose as a viscous ore fluid in centrifuge models, Geotechnical Testing Journal, (4), Tann, L. v. d., Tobita, T., and Iai, S. (). "Alicability of two stage scaling in dynamic centrifuge tests on saturated sand deosits." 7th International Conference on Physical Modelling in Geotechnics (ICPMG ), Sringman, Laue & Seward (eds), Terashi, M., Katagiri, M. and Ohishi, K. (4), Ten years centrifuge oeration at a consulting firm, International Journal of Physical Modelling in Geotechnics, 4(),. Tobita, T., Iai, S., and Noda, S. (9). "Study on generalized scaling law in centrifuge modeling with flat layered media." Proceedings of the 7th International Conference on Soil Mechanics and Geotechnical Engineering (7th ICSMGE), M. Hamza et al. (Eds.),

12 Tobita, T., Iai, S., and Tann, L. v. d. (). "Alication of the generalized scaling law to saturated ground." Submitted to the International Journal of Physical Modelling in Geotechnics. Tobita, T. and Iai, S. (), Limitation of methylcellulose as a viscous ore fluid in hysical model testing, (Under rearation for ublication.) Tokimatsu, K., Suzuki, H., Tabata, K. and Sato, M. (7), Three dimensional shaking table tests on soil-ile-structure models using E-Defense facility, 4th International Conference on Earthquake Engineering, June 5 8, Thessaloniki, Greece. White, D. J., Take, W. A. and Bolton, M. D. (3), Soil deformation measurement using article image velocimetry (PIV) and hotogrammetry, Géotechnique, 53(7), 飽和地盤に対する拡張型相似則の適用性 飛田哲男 井合進 要旨 Modeling of models の手法を用い, 動的遠心模型実験に用いられる拡張型相似則 (Iai, et al. 5) の適用性を検討する 実物の 分のの飽和砂質水平成層地盤を対象に, 遠心加速度を5gから7gに変化させ実験を行う 模型地盤に対し, プロトタイプスケールで最大入力加速度振幅.5m/s と3.m/s, 振動数.65Hz の正弦波を与えた いずれの実験ケースにおいても, 振動中の応答加速度, 水圧の挙動については, プロトタイプ換算値でほぼ一致した しかし, 振動後の過剰間隙水圧の消散過程において,g 以下の低い遠心加速度を用いた場合に,5g 以上の高い遠心場の場合と比較して, 消散時間が4 倍以上長くなる現象が見られた 低い遠心場では, 有効拘束圧が小さいため地盤の弾性係数が小さく, 圧密理論から予測されるように, 圧密時間 (= 水圧消散時間 ) が長くなるものと推察される キーワード : 遠心模型実験, 相似則, 液状化 36